1. Field of the Invention
The present invention relates generally to small scale mechanical oscillators, and relates more particularly to nanoscale mechanical oscillators with several vibrational elements that permit a number of resonance modes.
2. Description of Related Art
Microelectromechanical and nanoelectromechanical systems, MEMS and NEMS, respectively, are fabricated typically with semiconductor technology as mechanical devices. Some of their advantages include good resistance to thermal shock, electromagnetic radiation, and impact shock. As with typical mechanical structures, MEMS and NEMS structures possess natural vibrational frequencies that are determined by their exterior dimensions. For example, it is well known that a simple doubly clamped beam structure has a fundamental transverse resonance frequency determined by the equation
                    f        =                                            E              ρ                                ⁢                      t                          L              2                                                          (        1        )            
Where E is Young's modulus related to material stiffness, ρ is material density, t is a thickness dimension parallel to displacement and L is the length of the beam. Devices with dimensions on the order of microns typically have resonance frequencies on the order of tens of kilohertz up to a few megahertz. Devices with dimensions on the order of sub-micron levels have proportionally higher resonance frequencies in the gigahertz range. The high resonance frequencies available from MEMS and NEMS devices, with associated fast switching times, have been used successfully in a number of applications including mechanical switches and memory elements, mass or inertial sensors and other frequency-selective elements such as filters, mixers and amplifiers.
While MEMS devices have enjoyed popularity in a number of applications and benefited from a widespread effort in research, NEMS devices have not found as great a utilization. One difficulty in effectively applying NEMS devices to a given problem is that that the signal magnitude derived from operation of a NEMS device can be difficult to detect and signal strength can be significantly smaller than the counterpart MEMS devices. Because NEMS devices operate in a gigahertz range of frequencies, the small-scale responses are typically characterized by diminished amplitudes and increasing dissipative effects that result in a loss of signal fidelity. The signal losses are the result of numerous phenomena and are often well known. For example, the dissipative effects are increased by a heightened sensitivity to surface or processing induced defects in the silicon structures. The surface to volume ratio of the devices is increased thus making the sensitivity to defects more pronounced, and sensitivity to clamping losses derived from beam mounting points is also increased. Accordingly, losses that were small or negligible in MEMS devices become significant in the smaller NEMS devices as sensitivity to dissipative effect increases. The decrease in system size also leads to an increase in the effective stiffness of the structure, resulting in extremely small displacements even in resonance mode. Larger structures can provide high-order harmonics to overcome some of the size dependent effects, but the amplitude of high-order harmonics decreases rapidly with increasing harmonic order.
The difficulties in applying NEMS devices to produce mechanical RF and high-speed structures, for example, are thus highly challenging. Materials that can be challenging to work with, such as silicon carbide and diamond, provide higher sound velocities based on the stiffness-density ratio
                              E          ρ                                    (        2        )            
Other factors involved in providing a desired NEMS device include the length of the beam L, which should be on a sub-micron scale to obtain gigahertz frequency ranges. As the size of the oscillating beam decreases to the sub-micron scale, the relationship between elastic stiffness of the material and the structural dimensions results in difficult to detect femtometer-level displacements in the sub-micron structures.
Some techniques are available for detecting mechanical motion on the femtometer scale, such as coupling the resonator to an RF single electron transistor, or utilizing a SQUID sensor, a piezoelectric sensor or optical interferometry. These types of detection schemes typically have the object of enabling observation of quantum mechanical motion. However, the measurement sensitivity of the equipment at close to GHz frequencies in millikelvin temperatures continues to remain orders of magnitudes beyond the quantum mechanical signal size.
For example, observation of quantum behavior is governed by dissipation or energy relaxation of 1/Q. As structures become smaller, and thus stiffer, the spring constant k increases and the displacement at resonance, x=FQ\k decreases for a given amplitude of force F. Although it is desirable to obtain sub-micron scale mechanical devices to generate gigahertz range oscillations, it is also important to have a structure with relaxed characteristics to decrease the spring constant k to obtain a larger and detectable displacement. Simple gigahertz range beams produce small displacements at resonance that are very difficult to detect and it is difficult to de-couple the spring constant k from the beam natural frequency. The relationship between spring constant k and natural frequency produces signal dispersion influences that are difficult to overcome because the spring constant and the natural frequency are difficult to decouple. Accordingly, it is extremely difficult to realize a gigahertz frequency oscillator based on a vibratory structure, such as that of a beam.